Jessica is 2 times as old as Ashley. Twelve years ago, Jessica was 5 times as old as Ashley. How old is Jessica now?
Solution: We can use the given information to write down two equations that describe the ages of Jessica and Ashley. Let Jessica's current age be $j$ and Ashley's current age be $a$ The information in the first sentence can be expressed in the following equation: $j = 2a$ Twelve years ago, Jessica was $j - 12$ years old, and Ashley was $a - 12$ years old. The information in the second sentence can be expressed in the following equation: $j - 12 = 5(a - 12)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $j$ , it might be easiest to solve our first equation for $a$ and substitute it into our second equation. Solving our first equation for $a$ , we get: $a = j / 2$ . Substituting this into our second equation, we get: $j - 12 = 5($ $(j / 2)$ $- 12)$ which combines the information about $j$ from both of our original equations. Simplifying the right side of this equation, we get: $j - 12 = \dfrac{5}{2} j - 60$ Solving for $j$ , we get: $\dfrac{3}{2} j = 48$ $j = \dfrac{2}{3} \cdot 48 = 32$.